Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in PYTHON3):

Solution:
n = int(input())
if n == 1:
    print("NO")
else:
    # n = 1000000000
    triangular_numbers = []
    for k in range(1, 100000):
        triangular_numbers.append(int(k*(k+1)/2))
    last_limit = None

    high = len(triangular_numbers) - 1
    low = 0

    while True:
        mid = int((high + low) / 2)
        if high - low < 10:
            last_limit = high
            break
        else:
            if n < triangular_numbers[mid]:
                high = mid - 1
            elif n > triangular_numbers[mid]:
                low = mid + 1
            else:
                last_limit = triangular_numbers[mid]
                break

    last_index = last_limit
    found = False
    for a in triangular_numbers[:last_index+1]:
        b = n - a
        try:

            found = int((2*b + 0.25)**0.5 - 0.5) == (2*b + 0.25)**0.5 - 0.5 and int((2*b + 0.25)**0.5 - 0.5) > 0

        except:
            found = False
            break
        if found:
            print("YES")
            break
    if not found:
        print("NO")